In BiCG, the residual vector can be regarded as
the product
of and an th degree polynomial in , that is

This same polynomial satisfies
so that

This suggests that if reduces to a smaller
vector , then it might be advantageous to apply this
``contraction'' operator twice, and compute .
Equation () shows that the iteration coefficients can
still be recovered from these vectors, and it turns out to be easy to
find the corresponding approximations for . This
approach leads to the Conjugate Gradient Squared method (see
Sonneveld [192]).